In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.

翻译：本文研究一类可镇定且可检测随机系统的模型降阶技术。该方法基于一对格拉姆矩阵，我们从适定性角度对其进行分析。进而，利用这些格拉姆矩阵识别随机系统的优势子空间。我们提出了一种相关的平衡方案，通过剔除随机动态中的非重要信息来获得降阶系统。研究表明，该降阶模型保留了可镇定性与可检测性等重要特性。此外，基于格拉姆矩阵对乘积的特征值，进行了全面的误差分析。该分析为降阶质量提供了先验判据，并通过数值实验加以验证。